We included **HMH Into Math Grade 6 Answer Key PDF** **Module 16 Lesson 1 Explore Patterns of Data **to make students experts in learning maths.

## HMH Into Math Grade 6 Module 16 Lesson 1 Answer Key Explore Patterns of Data

I Can describe data distributions by their shapes.

**Spark Your Learning**

Sharice is collecting data on the lengths of crocodiles for a science project. She thinks it would help to make a poster for her class so the students can understand her data at a glance. How should she display her data?

American crocodiles: 5.0 m, 4.5 m, 3.0 m, 4.5 m

Australian freshwater crocodiles: 2.5 m, 2.0 m, 2.0 m, 1.5 m

Orinoco crocodiles: 4.5 m, 4.5 m, 2.5 m, 2.5 m

Answer:

Sharice can create a chart to display her data.

Name Mean Value Maximum Minimum

American crocodiles 4.25 m 5.0 m 3.0 m

Australian freshwater crocodiles 2.0 m 2.5 m 1.5 m

Orinoco crocodiles 3.5 m 4.5 m 2.5 m

**Turn and Talk** What are the advantages of visually organizing data?

Answer:

**Build Understanding**

Seeing data sets represented as dot plots and histograms can help you find and understand overall patterns in the data.

Question 1.

Mr. Ortega surveyed one of his classes to determine the number of siblings each of his students has. The results are summarized in the dot plot. What conclusions can you draw from the distribution of the data?

A. How many students did Mr. Ortega survey?

Answer:

2 students

Explanation:

There are 2 students Mr. Ortega surveyed.

B. A cluster is a group of data points that lie within a small interval. Does the dot plot have a cluster? If so, where?

Answer:

The dot plot has a cluster in 0, 1, 2.

C. A gap is an interval that contains no data. Does the dot plot have any gaps or deviations from the overall pattern? If so, where?

Answer:

4, 6, 8

Explanation:

Yes the plot have gaps from the overall patter. A gap that contains no data is 4, 6 and 8.

D. A peak is a data value which is higher than the values on either side. Does the dot plot have a peak? If so, where?

Answer:

The plot have a peak at 1.

Explanation:

The plot have a peak at 1 as the data value is higher than the values on either side.

E. Calculate the median of the data. How does it relate to the overall pattern?

Answer:

The median of the data is 4.

Explanation:

0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36

\(\frac{36}{9}\) = 4

F. Draw two conclusions from the survey results. Explain whether you used a cluster, gap, a peak, or a mode to reach each conclusion.

Answer:

**Turn and Talk** Suppose Mr. Ortega surveys all of his classes and summarizes the number of siblings in dot plots for each class. Would you expect the plots to look similar to the dot plot in Task 1 with respect to clusters and gaps? Explain.

Answer:

Question 2.

The histogram shows the fuel efficiency, in miles per gallon, for cars sold at Max’s Dealership.

A. Is there a peak in the distribution? If so, where?

Answer:

8

Explanation:

There is a peak in the distribution of frequency 8 and fuel efficiency.

B. Describe the pattern in how the data change across the intervals.

Answer:

In fuel efficiency from interval, 5-9 to 20-24 are increasing order and from intervals 25-29 to 35-39 are in decreasing order.

C. If you draw a vertical line through the middle of the interval 20-24, the two sides of the histogram are close to mirror images. So the histogram is nearly symmetric. Is the pattern in Part B an indicator of symmetry? Does the data deviate from the overall pattern? Explain.

Answer:

**Check Understanding**

**For Problems 1-2, describe the data set by identifying clusters, peaks, gaps, and symmetry. Draw one conclusion and explain how you reached it.**

Question 1.

Answer:

Clusters are from 0 to 3

Gaps 4, 5, 7, 8

Peaks – 1

symmetry – 1 is a line of symmetry.

Question 2.

Answer:

**On Your Own**

Question 3.

Construct Arguments The dot plot shows the number of hours that 40 students studied each week. Make a statement that describes the overall pattern of the data in the plot. Support your statement by describing clusters, gaps, and/or peaks.

Answer:

**For Problems 4 and 5,** describe any clusters, symmetry, peaks, and gaps or deviations from the overall pattern for the given distributions. Draw one conclusion about the data and explain how you reached it.

Question 4.

Answer:

Question 5.

Answer:

**I’m in a Learning Mindset!**

What can I apply from previous work to better understand patterns of data?

Answer:

**Lesson 16.1 More Practice/Homework**

Question 1.

Use Structure The histogram shows the fuel efficiency (in miles per gallon) for some automobiles. Make a statement that describes the overall pattern and the shape of the distribution. What conclusion can you draw?

Answer:

Question 2.

Describe any clusters, gaps, deviations from the overall pattern, and peaks. State the mode. Draw a conclusion based on these patterns in the data.

Answer:

Question 3.

Math on the Spot The data set and dot plot display the grades of Professor Burger’s students. Describe the shape of the data distribution.

Answer:

**Test Prep**

Question 4.

The dot plot shows the distribution of books read last summer by students at the Parks School. Which pattern in the data helps you conclude that most students read four books?

(A) a cluster

(B) a peak

(C) a gap

(D) no symmetry

Answer:

a peak

Explanation:

From the given data plot the peak is 4. So must students read four books. So the answer is peak.

Question 5.

In the survey from Problem 4, how many people were asked how many books they read last summer?

Answer:

9 people.

Explanation:

9 people were asked in the survey how many books they read last summer.

Question 6.

The histogram shows the distribution of petal lengths for flowers in a botanical garden. What statement best summarizes the data distribution?

(A) Most petal lengths are clustered at 1-1.9 centimeters.

(B) There is a symmetry between the short and long petal lengths.

(C) The majority of petal lengths are greater than 3.9 centimeters.

(D) There is a gap between 2 and 3.4 centimeters.

Answer:

The majority of petal lengths are greater than 3.9 centimeters.

**Spiral Review**

Question 7.

Evaluate the expression for x = 4 and y = 6. 4x – y + 15

Answer:

Given x = 4

y = 6

The equation is 4x – y + 15

simply the values in the given equation

(4 × 4) – 6 + 15

16 – 6 + 15

10 + 15

25.

Question 8.

Write an equation that models the data in the table.

Answer:

Question 9.

Simplify the expression: 4a + 8 – 2a – 4 + 7b.

Answer:

Given,

4a + 8 – 2a – 4 + 7b

4a – 2a + 8 + 7b – 4

2a + 4 + 7b

2a + 7b = -4